LECTURE 6: Factorial ANOVA

Research Methods in Psychology: Two-way Factorial ANOVA

Overview

  • Instructor: Samet Arslan

  • Course: Research Methods in Psychology, Week 6

Learning Objectives

Conceptual Parts

  • Define factorial ANOVA

  • Explore different types of factorial ANOVA

  • Understand factorial ANOVA as a statistical model and learn relevant jargon

  • Discuss main effects and interaction effects

Types of Factorial ANOVA

  • Between-subjects (BS): Independent groups

  • Within-subjects (WS): Repeated measures

  • Mixed factorial: Combination of BS and WS

Understanding Main Effects

Week 6 Focus

  • Examining designs and interpretations for between-subjects and within-subjects factorial ANOVA basics.

  • Expectation of deepening understanding through main and interaction effects in Week 7.

Conceptual Explanation of Factorial ANOVA

Definition

  • One-way ANOVA: Compares means across 3+ groups with 1 independent variable (IV) and 1 dependent variable (DV).

  • Two-way factorial ANOVA: Compares means across groups with 2 IVs and 1 DV, involving:

    • Two categorical IVs (each with two or more levels)

    • One continuous DV (e.g. scores on a scale)

Additional Types

  • Three-way factorial ANOVA: Involves 3 IVs and 1 DV; not covered this week,

    • Three categorical IVs

    • One continuous DV

Describing Factorial ANOVA Designs

  • Designs indicated by notation like 2 x 2, 2 x 3, 3 x 4, etc.:

    • Each number represents an IV

    • Numbers indicate levels in each IV

    • Example: 3 x 2 ANOVA has 2 IVs (IV1: 3 levels; IV2: 2 levels)

Three Types of Designs

Summary

  1. Between-subject factorial ANOVA: Each participant in one group only.

  2. Within-subject factorial ANOVA: Each participant assessed multiple times.

  3. Mixed factorial ANOVA: Involves both between-group and within-group factors.

ANOVA Model Expansion

Formula

  • F = Mean SSM / Mean SSR

  • Involves:

    • Main effect of IV1

    • Main effect of IV2

    • Interaction effect (IV1 x IV2)

Main Effects and Interaction Effects

Description

  • In a 2-way factorial ANOVA:

    • 3 effects total: 2 main effects (IV1 and IV2) and 1 interaction effect (IV1 x IV2)

  • Main Effect: Unique effect of an IV on the DV.

    • Example: Main effect of group independent of sex

  • Interaction Effect: Combined influence of both IVs on the DV.

Research Questions and Hypotheses

Example Questions

  1. Difference in depression scores between treatment types irrespective of sex?

  2. Do depression scores differ between males and females irrespective of treatment type?

  3. Do treatment type and sex interact in their effects?

Hypotheses

  • Expect main effect of treatment type

  • Expect main effect of sex

  • Expect interaction effect on depression scores.

Example: Two-way BS Factorial ANOVA

Topic

  • Effect of drug type and sex on risk-taking behavior.

Questions

  • Risk-taking behavior differences among drug users.

  • Impact of sex on risk-taking behavior.

Analysis

  • Assessment includes interaction between drug type and sex.

Steps to Conduct BS Factorial ANOVA in SPSS

Step 1: Data Entry

  • Enter/Export data correctly labeled as drug group and sex for DV of